In this section, we study the scattering angle considering an aligned spin binary system following [1]}.
First, we re-scale the spin variables as \(a_{(a)}=S_{(a)}/(m_{(a)}c)\) .
In the COM, the Hamiltonian \(\mathcal {H}\)  is expressed as a function of \(p_r\) , \(L\) , \(r\) , and \(S{(a)}\)  and inverting that we obtain
\(p_r=p_r(\mathcal {H},L,r,S_{(a)})\, .\) 
